Final answer:
The correct answer is b) invalid syllogism: affirming the consequent and c) invalid syllogism: denying the antecedent, as they do not guarantee the conclusion is true even if the premises are, unlike in a valid syllogism.
Step-by-step explanation:
Out of the options provided, b) invalid syllogism: affirming the consequent and c) invalid syllogism: denying the antecedent are both examples of common invalid inference forms. On the other hand, a valid syllogism is one where if the premises are true, the conclusion must be true as well. This is not the case with affirming the consequent and denying the antecedent because even with true premises, the conclusion may still be false. Examples of valid syllogism structures include the disjunctive syllogism, modus ponens, and modus tollens.